A072498 n is not equal to the product of the k smallest divisors of n for any k.

4, 9, 12, 16, 18, 20, 25, 28, 32, 36, 42, 44, 45, 48, 49, 50, 52, 54, 60, 63, 66, 68, 72, 75, 76, 78, 80, 81, 84, 88, 90, 92, 96, 98, 99, 100, 102, 104, 108, 110, 112, 114, 116, 117, 121, 124, 126, 128, 130, 132, 136, 138, 140, 147, 148, 150, 152, 153, 156, 160, 162

Offset

1,1

Comments

Positive integers not included in A072510. Sequence includes all squares of primes.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

Divisors of 384 are 1,2,3,4,6,8,12,16,24,32,48,64,96,128,192,384. Partial products are: 1=1, 1*2=2, 1*2*3=6, 1*2*3*4=24, 1*2*3*4*6=144, 1*2*3*4*6*8=1152 and so 384 (144<384<1152) is not in A072510.

Maple

filter:= proc(n) local F, d, p;
  F:= sort(convert(numtheory:-divisors(n), list));
  p:= 1:
  for d in F do
    p:= p*d;
    if p > n then return true
    elif p = n then return false
    fi
  od;
end proc:
select(filter, [$1..1000]); # Robert Israel, Sep 28 2016

Mathematica

Select[Range[200], !MemberQ[FoldList[Times, 1, Divisors[#]], #]&] (* Harvey P. Dale, Jun 18 2013 *)

Crossrefs

Cf. A072510.

Sequence in context: A094120 A066423 A355571 * A162643 A072587 A240112

Adjacent sequences: A072495 A072496 A072497 * A072499 A072500 A072501

Keyword

nonn

Author

Vladimir Baltic, Aug 03 2002

Extensions

Edited by Robert Israel, Sep 28 2016

Status

approved